On massive higher spins and gravity. IV. Arbitrary spin

TL;DR

This paper develops a framework for constructing gauge-invariant gravitational interaction vertices for massive fields of arbitrary spin, extending previous results to include all spins and partially massless limits.

Contribution

It introduces an ansatz for non-minimal interaction terms that yields a unique gauge-invariant vertex for any spin, generalizing earlier specific cases.

Findings

Successfully constructs gauge-invariant vertices for arbitrary spin fields.

Reproduces previous results for specific spins such as 5/2, 3, and 7/2.

Includes all possible partially massless limits.

Abstract

In this paper, we investigate gravitational interactions of massive fields with arbitrary integer and half-integer spin, trying to construct a vertex that contains both standard minimal and non-minimal interaction terms necessary to make the vertex gauge invariant. We propose an ansatz for these non-minimal terms and show that it leads to a unique solution that correctly reproduces our previous results for spins 5/2, 3 and 7/2, including all possible partially massless limits.